Chapter 2: FAQs 189
This simple example illustrates the subtlety of the whole
valuation/pricing process. In many ways options are like
go-carts and valuable insight can be gained by thinking
on this more basic level.
The quant rarely thinks like the above. To him value
and price are the same, the two words often used inter-
changeably. And the concept of worth does not crop up.
When a quant has to value an exotic contract he looks
to the exchange-traded vanillas to give him some insight
into what volatility to use. This iscalibration. A vanilla
trades at $10, say. That is the price. The quant then
backs out from a Black–Scholesvaluationformula the
market’s implied volatility. By so doing he is assuming
that price and value are identical.
Related to this topic is the question of whether a math-
ematical modelexplainsordescribesa phenomenon.
The equations of fluid mechanics, for example, do both.
They are based on conservation of mass and momen-
tum, two very sound physical principles. Contrast this
with the models for derivatives.
Prices are dictated in practice by supply and demand.
Contracts that are in demand, such as out-of-the-money
puts for downside protection, are relatively expensive.
This is theexplanationfor prices. Yet the mathematical
models we use for pricing have no mention of supply
or demand. They are based on random walks for the
underlying with an unobservable volatility parameter,
and the assumption of no arbitrage. The models try
todescribehow the prices ought to behave given a
volatility. But as we know from data, if we plug in our
own forecast of future volatility into the option-pricing
formulæ we will get values that disagree with the market
prices. Either our forecast is wrong and the market
knows better, or the model is incorrect, or the market